I posted it on Facebook, and got a bunch of suggestions as to what it might be, and who might be able to help - including a few that it might be Hebrew instead.
Hebrew looks like this:
while Arabic looks like this:
And the symbols in the image looked more like the curves of Arabic than the angles of Hebrew. But a few people also suggested Masonic symbols, so I walked back down the road after we got home and took another, better photo:
Okay, yes, that's clearly the letter's J and D, with some squiggly bits around them because the architect was all posh and stuff. No historical mystery at all. Dangit.
Original post on Dreamwidth - there are comments there.